Anisotropic Multicenter Bonding and High Thermoelectric

Article pubs.acs.org/cm

Anisotropic Multicenter Bonding and High Thermoelectric Performance in Electron-Poor CdSb Shanyu Wang,†,⊥ Jiong Yang,†,⊥ Lihua Wu,† Ping Wei,† Jihui Yang,*,† Wenqing Zhang,*,‡ and Yuri Grin*,§ †

Materials Science and Engineering Department, University of Washington, Seattle, Washington 98195-2120, United States Materials Genome Institute, Shanghai University, Shanghai 200333, China § Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany ‡

S Supporting Information *

ABSTRACT: Long-standing challenges to simultaneously accomplish crystal-like electrical transport and glass-like thermal transport in materials hinder the development of thermoelectric energy conversion technologies. We show that the unusual combination of these transport properties can be realized in electron-poor II−V semiconductor CdSb. Anisotropic multicenter bonding in CdSb is essential to both electrical and thermal transport. The electrondeficiency-sharing multicenter interactions lead to low overall ionicity and hence relatively high carrier weighted mobility and power factor. The bond anisotropy causes large lattice anharmonicity, which coupled with low cutoff frequency of the longitudinal acoustic branch and low sound velocity, gives rise to intrinsically low lattice thermal conductivity, approaching the glass-limit at elevated temperatures. A maximum thermoelectric figure of merit ZT of ∼1.3 at 560 K and an average ZT of 1.0 between 300 K and 600 K are achieved for the 0.5 at. % Ag-doped sample, which makes CdSb an attractive candidate for low-intermediate temperature or multistage power generations. Our study advocates the search for high efficiency thermoelectric materials in compounds with anisotropic two- and multicenter bonding.

1. INTRODUCTION Narrow gap semiconductors with intrinsically high carrier weighted mobility (U = μ(md*/m0)3/2, where μ is the carrier mobility, md* the density of states effective mass, and m0 the free electron mass) and low lattice thermal conductivity (κL) are promising candidates for thermoelectric power generation or heating/cooling applications.1 The electron and phonon transport properties are fundamentally dominated by the natures of crystal structure and chemical bonding. High U is generally achieved in materials with low ionicity and high band degeneracy (Nv) such as Bi2Te3, PbTe, CoSb3, etc. Meanwhile, intrinsically low κL originating from lattice features, such as complex crystal structure with heavy constituents,2,3 strong lattice anharmonicity,4−8 soft bonding,9−13 or the guestframework interactions and ordering,14,15 is of particular interest due to its robustness with respect to impurity level, grain size, crystallinity, or other structural variations. Thus, identification or understanding of lattice-bonding characteristics responsible for concurrently high U and intrinsically low κL not only is a fundamental challenge of electrical and thermal transports in solids, but also has important implications in designing high efficiency thermoelectric materials. Lattice anharmonicity, which arises from the nonlinear atomic interactions and controlling the phonon−phonon © 2015 American Chemical Society

Umklapp and Normal scattering processes, has drawn great interest.4,5,16 Large lattice anharmonicity has been reported in many types of compounds such as near ferroelectric materials17,18 and compounds with weakly bonded16,19 or even nonbonded electrons (e.g., electron lone pairs4,5,8). Among these materials, the electron-rich lone pair compounds, such as Cu3SbSe3,20 show minimum κL due to the strong Coulombic repulsion of the electron lone pairs under lattice distortions; but their low U values generally lead to poor electrical and thus poor thermoelectric properties.4 Analogous to the electron-rich lone pair systems, electron-poor compounds with average valence electrons per atom less than four, however, could feature concurrent low κL and high U with unique multicenter bonding scheme.21,22 This is because the easily deformed electron density within the multicenter bonds causes soft bonding and large lattice anharmonicity; meanwhile, the electron-deficiency-sharing effect of the multicenter bonds lowers the overall ionicity and ensures high U.22 This “high U− low κL” feature in multicenter bonded compounds is robust and Received: November 30, 2014 Revised: January 2, 2015 Published: January 5, 2015 1071

DOI: 10.1021/cm504398d Chem. Mater. 2015, 27, 1071−1081

Chemistry of Materials

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Figure 1. Crystal structure of CdSb: (a) unit cell with the bonds shorter than 3.0 Å; (b) atomic environment of atoms as well as the bonding lengths and angles, (c) projection along the [001] direction with the vertical dotted lines designating the cleavage planes, (d) shape and effective charges of the QTAIM atoms.

for the 0.5 at. % Ag-doped CdSb sample, which make it a promising material for low-intermediate temperature or multistage power generations.

ideal for thermoelectrics, which would offer a new perspective for designing novel thermoelectric materials. The materials of interest are binary II−V group antimonides with 1:1 atomic ratios such as ZnSb23,24 and CdSb.25,26 Both of them are typical electron-poor compounds according to their number of valence electrons (2 + 5 = 7). For ZnSb, firstprinciples calculations revealed an unique localized weak multicenter bonding (four center−four electron, 4c−4e) within the Zn2Sb2 rhomboid ring.22,27 Experimentally, ZnSb shows much lower κL (∼1−2 W/m K at 300 K) than the tetrahedrally bonded GaSb (κL ∼35 W/m K at 300 K)28 and ZnTe (κL ∼18 W/m K at 300 K),29 and much higher U (∼50−100 cm2/V s)23,31 than the lone-pair compounds.4,20 The correlations between the transport properties of ZnSb and its multicenter bonding scheme, however, are missing in the literature.9,22 The bonding scheme of CdSb, presumably possessing substantial similarity to that of ZnSb, until now has never been verified by quantum chemical or density functional calculations. Previously proposed bonding models were given without concrete justifications and could not account for the majority of physical phenomena observed.30−34 In addition, single-crystal CdSb indeed shows promising electrical and thermal transport properties,35,36 yet the bonding-property relation in CdSb has not been systematically studied. In this work, we present a quantum chemical treatment of atomic interactions in CdSb, which reveals a complex covalent multicenter bonding scheme. The electron-deficiency-sharing effect of multicenter bonding lowers the overall ionicity as expected and thus gives rise to measured high weighted mobility U in polycrystalline CdSb. The easily deformed charge density and the electron-deficient nature of the multicenter bonding lead to unique lattice dynamics, including large lattice anharmonicity, strong acoustic-optical coupling, and low sound velocity, which all contribute to its very low κL. The resulting high U and low κL bring about a maximum ZT of 1.3 at 560 K

2. RESULTS AND DISCUSSION 2.1. Crystal Structure and Chemical Bonding. The orthorhombic unit cell of CdSb contains eight CdSb formula units (Figure 1a). Here, only the bonds with the interatomic distances lower than 3.0 Å are shown. All Cd and all Sb atoms are equivalent in the structure. At the first glance, they seem to be tetrahedrally bonded, and the interatomic distances and bonding angles around Sb are labeled in Figure 1b according to ref 31. As shown in Figure 1b, for each Sb and Cd there are five neighbor atoms within the range of interatomic distances 2.793−3.136 Å defined by the sum of metallic radii of Cd (1.56 Å) and Sb (1.61 Å) (including four heteroatomic Cd−Sb and one homoatomic Sb−Sb or Cd−Cd). Only three shortest contacts for each Sb (two Cd−Sb and one Sb−Sb with the interatomic distances in the range of 2.793−2.824 Å (Figure 1b)), however, are comparable to the sum of covalent radii of Cd (1.44 Å) and Sb (1.39 Å). Meanwhile, for each Cd atom, there are only two short Cd−Sb contacts (2.824 and 2.793 Å) within the “covalent” range. Another interesting structural feature is the existence of cleavage planes perpendicular to the [100] direction, which can be attributed to the weak interactions between layers, as shown in Figure 1c.32,33 A good starting point for understanding the chemical bonding in CdSb is to analyze chemical analogs, which can be described in accordance with the usual valence rules.37 Therefore, for sphalerite-type crystal structures of CdS or CdSe in which all atoms are tetrahedrally coordinated, one needs on average four electrons per atom to form all the existing bonds as two-center−two-electron (2c−2e) bonds. Reducing the number of electrons while keeping the component ratio of 1:1 1072



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Figure 2. Electron-localizability indicator (ELI-D, ϒ) in CdSb: (a,d) ELI-D basins of the two-center Cd−Sb bonds; (b) ELI-D distribution along the two-center Cd−Sb and Sb−Sb contacts; (c) ELI-D basin of the Sb−Sb bond; (e) ELI-D distribution in the plane of the Cd−Sb contacts; (f) ELI-D basin of the three-center Cd−Sb−Cd interaction; (g) isosurface with ϒ = 1.18 visualizing positions of ELI-D attractors on the Sb−Sb contact and within the Cd−Sb−Cd triangles.

observed.41 The integration of electron density within the sodefined atomic volumes yielded relatively low charges of Cd (+0.18) and Sb (−0.18) being practically independent of the calculation techniques (LAPW, LMTO-ASA, FPLO, or Bader charge42). The charge transfer within the CdSb lattice is even much smaller than that of InSb (Bader charge: 0.31), although Cd (1.69) is more electropositive than In (1.78).44 These relatively low charge transfer of CdSb mainly relates to the unique bonding scheme and charge distribution, as discussed below. The electron-localizability indicator (ELI-D45,46) was shown to be a suitable quantum-chemical tool for visualizing multicenter interactions.41 Spherical distribution of ELI-D in the penultimate shells of Cd and Sb (Figure 2b,e) reveals, as expected, that they do not participate in the bonding within the valence region. In contrast to the isolated atoms, the last shells of Cd and Sb are not observed as separated spherical topological objects; they are strongly structured. In the valence region, there are five types of ELI-D maxima formed. The first one is located on the shortest Sb−Sb contacts (Figure 2b,g). The combined analysis of charge density and ELI-D reveals that the basin of this attractor is completely located in equal halves within the QTAIM basins of the neighboring antimony atoms. In the ELI-D representation, the basin of this attractor has common surface only with the core basins of the antimony atoms (Figure 2c). Thus, this attractor represents a 2c−Sb−Sb bond. The remaining four attractors are located within the triangles Cd−Sb−Cd (Figure 2g) and at the first look may represent the according 3c interactions. To confirm this

constant makes it impossible to form all bonds as 2c−2e interactions. One way to satisfy the electronic needs in such cases, for example, in NaP, NaSi, or NaTl, is described by the Zintl−Klemm concept.38,39 The concept assumes the formation of a cationic and an anionic part of the crystal structure. The electrons of the cations are transferred to the anionic substructure (charge transfer due to the large electronegativity difference between the components) and are used there for the formation of 2c−2e covalent bonds. The interaction between these substructures is an ionic one. In case of low average electron numbers per atom, the other way of structural organization is formation of the multicenter (mainly threecenter) bonds in the anionic substructure if the difference in electronegativity is large enough (e.g., in CaB640) or in the whole structure if the charge transfer is relatively small (e.g., in Al5Co241). The first-principles calculations in this study were carried out using TB-LMTO-ASA and FPLO-942 program packages. Computational details are presented in the Supporting Information. To explore the organization of atomic interactions in CdSb, quantum chemical techniques of bonding analysis in real space were applied. Analysis of the total electron density in CdSb by applying the Quantum Theory of Atoms in Molecules43 (QTAIM, Figure 1d) reveals atomic basins with the shape strongly deviating from the spherical one, which would be expected for an ionic interaction. Moreover, the shapes of the so-obtained QTAIM atoms reflect their atomic environment and are very similar to that of Co and Al in Al5Co2 where a large amount of three- and four-center interactions were 1073



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thermoelectric transport properties of polycrystalline CdSb samples are roughly isotropic, as shown in Figure S7. Low temperature (4−300 K) Hall coefficients and mobilities of Cd1−xAgxSb polycrystals are shown in Figure 3a and 3b, respectively, and the corresponding 300 K data are summarized in Table 1. Ag-doping significantly increases the hole

assumption, the basins of these attractors were analyzed for their synapticity, i.e., with which core basins they have common surfaces.47 The basin of the attractor located in the triangle Cd(1)−Sb−Cd(2) (Figure 2g) has indeed common surfaces with all three atomic core basins (Figure 2f). Thus, it represents a 3c interaction. The basin of the attractor in the triangle Cd(2)− Sb−Cd(3) has, contrary to its location, the common surfaces only with two core basins, Cd(3) and Sb (Figure 2d). It is disynaptic and represents a 2c bond Cd−Sb. Both basins of attractors located in the triangles Cd(1)−Sb−Cd(4) and Cd(4)− Sb−Cd(3) have common surfaces only with the core basins of Cd(4) and Sb, thus representing both the two-center interaction Cd(4)−Sb. Such a splitting of the expected torus-like basin around the Cd(4)−Sb46 line is caused by the reduction of the local symmetry in respect of the cylindrical one and is often observed in intermetallic compounds, for example, in Al5Co2.41 In total, the organization of the bonding in CdSb can be described as a coexistence of covalently bonded (2c bonds) Sb2 dumbbells, which are interconnected by 2c Cd−Sb bonds (Cd(3)−Sb and Cd(4)−Sb) into a two-dimensional layer running perpendicular to the [100] direction. The layers are interconnected to a three-dimensional framework with the 3c interactions (Cd(1)−Sb−Cd(2)). If one would consider these 3c bonds as a shared lone pair, the bonding situation becomes similar to that in Bi2Te3, where the covalently bonded layers are separated by the regions with van der Waals interactions between the lone pairs. In other words, CdSb represents a topological bonding analogous to the basic thermoelectric material Bi2Te3. In comparison with the sphalerite-type CdSe and CdS, the coordination number of Sb increases to five (four heteroatomic Cd−Sb and one homoatomic contact Sb−Sb), and the coordination number of Cd is formally also five, but only the four antimony ligands are connected to the central Cd via 2c and 3c bonds. Appearance of the 3c bonds in comparison with the sphalerite-type structure pattern is caused by the electron demand (3.5 electron par atom) with respect to a system of four-bonded atoms with four electrons per atom. The clear anisotropy of the chemical bonding in CdSb may explain the cleavage behavior, phononic, and anisotropic electronic transport. The low thermal conductivity,48 larger thermal expansion, thermal vibration, and lower hole mobility along the [100] direction are mainly due to the bonding anisotropy, being again analogous to the van der Waals gap in Bi2Te3.10 The combined 2c- and 3c-bonding model in CdSb obtained by our quantum chemical calculations is similar to the scenario suggested for ZnSb (4c−4e) but shows apparent difference in the multicenter contribution.22 Most importantly, these unusual features, such as anisotropic multicenter bonding, low ionicity, cleavage planes, etc., are believed to have significant impacts on the thermal and electrical transport properties, which will be discussed in the following sections. 2.2. Hole Mobility and Weighted Mobility. Because of the electron-deficiency-sharing effect within the multicenter bonds leading to the weak ionicity, it is reasonable to expect that the special bonding could ensure a high carrier mobility. To verify the effects of multicenter bonding on the carrier and phonon transports, a serial of Ag-doped CdSb polycrystalline samples was prepared. Here, Ag-doping is used to adjust the hole concentration. The X-ray diffraction (XRD) patterns and microstructural characteristics, shown in Figures S1 and S3−S6 (Supporting Information), indicate good phase and composition homogeneities. Figure S2 is the phase diagram of the binary Cd−Sb system. Furthermore, the microstructure and

Figure 3. (a) Low temperature (2−300 K) hole concentration and (b) mobility of Cd1−xAgxSb, and the dashed and solid lines in panel b represent μ ∼T −3/2 (acoustic phonon scattering) and μ ∼T 3/2 (ionized impurity scattering), respectively. (c) Comparisons of U/Nv of the electron-poor CdSb and ZnSb (Nv = 2)24 with those of (Bi,Sb)2Te3 (Nv = 6),56,62−64 PbTe (Nv = 4),65,66 SiGe (Nv = 3)67 and typical lone-pair compounds (AgSbTe2 (Nv = 6),68,69 Cu3SbSe3 (Nv = 1)20). 1074



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Table 1. Hall Coefficients RH, Carrier Concentrations pH, Mobilities μH, Seebeck Coefficients α, Reduced Fermi Levels (η = EF/ kBT), Calculated Effective Masses md*/m0 Based on the Assumption of Single Parabolic Band and Mixed Scattering (Mixed Ionized Impurity and Acoustic Phonon Scattering, Sattering Parameter s = 1), and Weighted Mobilities (U) at 300 K for Cd1−xAgxSb (x = 0.0−1%) Samples samples x x x x x

= = = = =

0.0 0.1% 0.3% 0.5% 1.0%

RH (cm3/C)

pH (1019 cm−3)

μH (cm2/V s)

α (μV/K)

η (s = 1)

md*/m0 (s = 1)

U (cm2/V s)

10.2 0.52 0.48 0.43 0.36

0.06 1.2 1.3 1.5 1.8

520 180 210 210 170

400 203 200 195 180

−1.57 1.41 1.48 1.59 1.94

0.25 0.38 0.39 0.41 0.41

65 43 51 54 45

Figure 4. Temperature dependence of thermal transport properties of Cd1−xAgxSb, (a) thermal conductivity, (b) lattice thermal conductivity with bipolar contribution at elevated temperature. The solid line in panel b is calculated based on phonon dispersion and γq using the Debye−Callaway model, and the dashed line represents the minimum lattice thermal conductivity of CdSb.

valence band degeneracy of CdSb (Nv = 2).35,50 Here, the effective masses for U calculations are estimated based on the assumptions of single parabolic band and mixed scattering of carriers (scattering parameter s = 1, which is an intermediate value of those of ionized impurity (s = 2) and acoustic phonon scattering (s = 0)). The methodology can be found elsewhere.58,59 The calculated results based on the simple assumption could probably show some error due to the band nonparabolicity, band degeneracy, or complex scattering processes, whereas they can still reveal some valuable insight about the band structure evolution upon Ag-doping. The calculated density of states effective mass, increasing from 0.25m0 to 0.41m0 with increasing hole concentration, is well consistent with the band nonparabolicity and previous studies,25,50,60,61 which also indicates the rational choice of the scattering parameter s = 1. To exclude the influence of band degeneracy Nv on U, U/Nv was calculated to show the weighted mobility of a single band pocket. Comparisons of U/Nv versus carrier concentration among polycrystalline compounds are shown in Figure 3c, including the electron-poor CdSb and ZnSb24 and p-type state-of-the-art ((Bi,Sb)2Te3 (Nv = 6),56,62−64 PbTe (Nv = 4),65,66 and SiGe (Nv = 3)67) and typical lone pair compounds (AgSbTe2 (Nv = 6),68,69 and Cu3SbSe3 (Nv = 1)20). The lone-pair systems, especially Cu3SbSe3,20 show very low U/Nv values less than 10 cm2/V s, also evidenced by their relatively large ionicity according to our Bader charge analyses (Cu3SbSe3:Cu +0.17, Sb +0.7, Se −0.4). The multicenter bonded electron poor CdSb and ZnSb, however, show much higher U/Nv values (30−40 cm2/V s), which are comparable to those of state-of-the-art thermoelectric compounds, as shown in Figure 3c. The electron-deficiency-

concentration, but the hole concentration does not increase linearly as the Ag content increases, as shown in Figure S8. The temperature exponent of hole mobility is ∼3/2 above 100 K, which indicates the dominance of ionized impurity scattering on hole transport. Around 300 K, the temperature exponents for some samples deviate from 3/2, which signifies the growing influence of carrier acoustic phonon scattering. This temperature dependence is distinct from those of single crystals (all showing a negative temperature exponent ranging from −1 to −1.5), including the nondegenerate undoped or degenerate heavily doped samples. The scattering mechanisms of single crystals can be identified as acoustic phonon scattering (undoped) or mixed scatterings by acoustic phonon and ionized impurity (heavily doped).33,35,36,49−52 On the basis of the Brooks−Herring formula of ionized impurity scattering mobility,53 we conclude a much higher impurity density or large degree of compensation for the polycrystals. The source of ionized impurities could be intrinsic defects such as Cd or Sb vacancies generated by plastic deformations,54 similar to the case of Bi2Te3-based materials.55 This is also substantiated by the much higher hole concentration of our undoped polycrystal (∼6 × 1017 cm−3) as compared to the single crystals (1015−1016 cm−3).33,35,36,49−52 As mentioned, the electron-deficiency-sharing within the multicenter bonds ensures low ionicity and thus high carrier mobility and weighted mobility U.1,2 As shown in Figure 3b, even with strong ionized impurity scattering, CdSb polycrystals still show high mobilities, ∼200 cm2/V s, comparable to those of the state-of-the-art thermoelectric materials.56,57 More importantly, the calculated U values of ∼40−65 cm2/V s, as shown in Table 1, are reasonably high considering the low 1075



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Table 2. Phonon Velocities in the Vicinity of Brillouin Zone Center (vLA, vTA1, vTA2), Average Mode Grüneisen Parameters (γL̅ A, γT̅ A1, γT̅ A2), Debye Temperatures (ΘLA, ΘTA1, ΘTA2) for Longitudinal (LA) and Transverse (TA1, TA2) Acoustic Phonon Branches along the Γ−X, Γ−Y, and Γ−Z Directions. The Mode Debye Temperature Is Calculated Using Θ = ℏωcut‑off/kB, where ωcut‑off Is the Highest Frequency, and kB Is the Boltzmann Constant. The Average Phonon Velocities, Mode Grüneisen Constants, and Debye Temperatures Are Taken as the Average Values of the Three Directions directions

vLA (m/s)

vTA1 (m/s)

vTA2 (m/s)

Γ-X Γ-Y Γ-Z average

2824 3050 3090 2988

1368 1351 1180 1300

1654 1445 1645 1581

γL̅ A 2.52 2.12 1.72 2.12

γT̅ A1 0.62 2.64 0.40 1.22

γT̅ A2 0.42 0.20 0.78 0.47

ΘLA (K)

ΘTA1 (K)

ΘTA2 (K)

48 38 45 44

43 36 35 38

42 31 35 36

Figure 5. (a) Phonon dispersion relation of CdSb along some high symmetry lines; (b) total phonon density of states and partial contributions from Cd and Sb; (c) mode Grüneisen parameters of acoustic branches along the Γ−X and Γ−Z directions, the inset in panel c shows the synergistic movement (TA1) along the a direction (the weak Cd−Sb bonds are not shown for better visualization).

than those of some of binary thermoelectric compounds, for example, Bi 2 Te 3 ,73 PbTe, 74 and In 4 Se 3 75 with heavier constituents or more complex structures, as shown in Figure S10 (Supporting Information). In addition, κL of doped samples roughly follow a T−1 dependence in the measurement temperature range, which is indicative of the dominant phonon−phonon Umklapp processes. The minimum κL of CdSb can be estimated using the model developed by Cahill et al:76

sharing effect among multiple atoms significantly lowers the overall ionicity in CdSb (low charge transfer of ∼0.18 as shown in Figure 1d), even with a relatively large electronegativity difference (Δχ ≈ 0.4). The comparable U/Nv values of CdSb to state-of-art thermoelectric compounds with smaller Δχ (∼0.08 for Bi2Te3, ∼0.2 for PbTe, ∼0.1 for SiGe) also validate the beneficial effect of multicenter bonding on electrical transport, in sharp contrast to the detrimental influence of lone electron pair (e.g., low Δχ < 0.2 but comparable Bader charges (Ag +0.18, Sb +0.25, Te −0.21) for AgSbTe2). 2.3. Thermal Transport Property and Phonon Dispersion. The multicenter-bonded materials also show very low thermal conductivity. The temperature dependence of thermal transport properties of polycrystalline Cd1−xAgxSb is shown in Figure 4. Here, the lattice thermal conductivity κL is calculated by subtracting the carrier contribution κe from the total thermal conductivity κ, and κe is estimated using the Wiedemann− Franz law κe = LσT, where the Lorenz number L is chosen to be 2.0 × 10−8 V2/K2, and σ and T are the electrical conductivity and absolute temperature, respectively. All samples show low κ values of 1.0−1.2 W/m K at 300 K, which are slightly lower than those of single crystals with comparable electrical conductivity (∼1.5 W/m K at 300 K36) due to the intensified phonon defect scatterings. The undoped sample shows a κL value of 1.0 W/m K at 300 K as expected and visible bipolar thermal transport at elevated temperatures. Ag-doping not only slightly decreases κL because of the increased point defect or electron−phonon scatterings, but also clearly mitigates the bipolar thermal transport by increasing the majority carrier concentration.70 These κL values of ∼0.8−1.0 W/m K at 300 K are significantly lower than those of zinc-blend CdTe (7.5 W/m K at 300 K)71 or InSb (18 W/m K at 300 K)72 and also lower

κ min

⎛ T ⎞2 ⎛ π ⎞1/3 2/3 ⎜ ⎟ = kn ∑ vi⎜ ⎟ ⎝6⎠ B a ⎝ θi ⎠ i

∫0

θi / T

x 3e x dx (e x − 1)2

(1)

where the summation is over the three polarization modes, and kB is the Boltzmann constant. The mode Debye temperature (in units of K) θi = vi (ℏ/kB)(6π2na)1/3, where na is the number density of atoms (∼3.52 × 1022 cm−3 for CdSb), ℏ the reduced Planck constant, vi the sound velocity for each polarization mode, and i the polarization index. By using the calculated sound velocities derived from phonon dispersions listed in Table 2 (discussed below), the estimated κmin is shown as the dashed line in Figure 4b. At elevated temperatures, κL of doped samples (∼0.4−0.5 W/m K) approaches the κmin of CdSb (∼0.35 W/m K). The intrinsically low κL should be related to the unique lattice dynamics associated with the anisotropic multicenter bonding. To shed light on the effects of anisotropic multicenter bonding on phonon transport, the phonon dispersion relation, projected phonon density of states, and mode Grüneisen parameters (γq,i = −(V/ωq,i) (∂ωq,i/∂V), q corresponds to the wave vector and i the branch index) of acoustic phonon branches of CdSb are calculated, as shown in Figure 5. Phonon 1076



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Figure 6. (a) Electronic band structure of CdSb and (b) corresponding total density of states and partial contributions from Cd and Sb, partial band structures projected on (c) Cd and (d) Sb atoms, vertical bars superimposed on band structures represent the strength of band characters from certain atoms.

spectra under equilibrium volume V0 and 0.99 V0 are used for the calculations of γq,i. The longitudinal acoustic branch (LA) interacts with low-lying optical branches along multiple directions in the first Brillouin zone (BZ), and an obvious avoided-crossing feature can be observed, as illustrated in Figure 5a. These optical branches that interact strongly with LA can be pertained to the shearing movement of four atom layers (tetrads with two slabs) along the (100) cleavage planes. These effects lead to abrupt changes of slope at approximately midway of the BZ to the zone boundary and low average cutoff frequency of ∼3.2 meV for the LA branch. Although the lowlying optical phonon mode is common to many layered compounds, such as Bi2Te3 where the lowest optical mode is the synergistic shearing of quintuples along the van der Waals gaps,77,78 the avoided-crossing characteristic of optical-acoustic interactions is seldom observed and absent in Bi2Te3. The two transverse acoustic branches (TA1 and TA2), however, have normal behaviors with no interaction with the optical phonon branches, and maximal frequencies are ∼3 meV at the BZ boundary. The zone center group velocities of acoustic phonon branches are calculated for the Γ−X, Γ−Y, and Γ−Z directions, respectively, as shown in Table 2. The average sound velocity vg̅ is estimated to be ∼1590 m/s (average for the three directions), which is well consistent with the experimental results.79 This value is comparable to that of Bi2Te3 (1620 m/ s)80 and smaller than those of PbTe (1770 m/s),81 CdTe (1743 m/s),82 ZnSb (2241 m/s), and Zn4Sb3 (1805 m/s).9 According

to a harmonic approximation, the average phonon group velocity should be proportional to the root square of average force constant (β). It is clear that the low vg̅ of CdSb is mainly attributed to the small β value (as well as moderately heavy constituents) and indicates weak bonding as expected for threecenter interactions. The weak bonding is also consistent with the small Young’s modulus (55−60 GPa) of CdSb.83 On the basis of our analyses of the bonding scheme, the existence of cleavage planes perpendicular to the a axis should relate to the multicenter bonds (3c−2e), especially along the crystallographic [100] direction. This anisotropic multicenter bonding is a direct consequence of the electron-poor nature of CdSb (3.5 e/atom), in contrast to the tetrahedrally sp3-bonded InSb and CdTe (4 e/atom). For phonon transport dominated by the Umklapp processes, the relaxation time τU is inversely proportional to the square of Grüneisen parameter γ2. The calculated γq,i shown in Figure 5c displays both positive and negative values, and different branches show distinct γ values, even for the same branch along different BZ directions. Remarkably, TA1 along the Γ−Z direction (crystallographic c direction) shows anomalously large Grüneisen parameter near the zone center, which indicates that this branch is rather anharmonic. In addition, the LA branch, especially along the Γ−X direction, also has large γ values. Analysis of the eigenvectors indicates that the two strongly anharmonic TA1 and LA branches pertain to the synergistic movements perpendicular to the (100) cleavage plane (crossplane motion), which contains the multicenter bonds, as 1077



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Figure 7. Temperature dependences of electrical transport properties of Cd1−xAgxSb, (a) electrical conductivity, (b) Seebeck coefficient, (c) room temperature Seebeck coefficient versus hole concentration, (d) power factor (α2σ); the solid line in , panel c is calculated based on the band structure shown in Figure 6, panel a and the Boltzmann transport theory under a rigid band approximation.

The large lattice anharmonicity of the electron-poor system is analogous to that of electron lone pair systems (Cu3SbSe3 or AgSbTe2),6,86 and the two types of systems share a similar feature that is the existence of easily deformed charge density. The strong interactions between these easily deformed charge density and lattice waves are the origin of large lattice anharmonicity, in spite of their opposite scenarios in terms of the electron shell completeness (one is electron-deficient and the other electron-rich in contrast to tetrahedrally bonded atoms with electronic octets). Our work manifests another possible source of strong lattice anharmonicity in crystalline covalent compounds with electron-deficient multicenter bonds. The magnitude of lattice anharmonicity is mainly determined by the strength of the multicenter bonds, which is related to their charge densities (number of electrons involved) and spatial distributions (volumetric density of electrons). Furthermore, this intrinsically low κL of CdSb, absence of other phonon scattering mechanisms such as nanostructuring, is more easily reproduced, and the particular bonding scheme and crystal structural features reveal a new avenue for designing high efficiency thermoelectric materials with intrinsically low κL. 2.4. Electronic Band Structure and High T Electrical Transport Property. The electronic band structure along some high symmetry lines and the density of states (DOS) of CdSb are presented in Figure 6. The modified Becke−Johnson (mBJ) potential was adopted for band-gap correction,87,88 and the calculated value is 0.47 eV, well consistent with the results determined from electrical resistivity and optical absorption coefficient.25,89−91 The valence band maximum (VBM) is off the high symmetry lines, close to the X point (along the Γ−X direction). In addition, there is a slightly heavier hole band

indicated in the inset of Figure 5c. The average Grüneisen parameters (γ)̅ are also calculated by the method described by Morelli et al.,84 as shown in Table 2. It is clear that TA1 along the Γ−Z direction and LA along the Γ−X direction show very large γ ̅ values of 2.64 and 2.52, respectively. These values are significantly larger than that of strong covalent bonds (γ ∼1.0, as reported in diamond and silicon85) and even pure ionic bonds (∼2.2),19 and the origin of this large anharmonicity can be traced to the weak multicenter bonds with easily deformed charge density. The internuclear spaces and thus force constants of these weak multicenter bonds would show large electrostatic response to displacements of atoms by lattice wave distortions, resulting in strong bonding anharmonicity and thus large γ.19 The anisotropic distribution of delocalized multicenter charge density as shown in Figure 2, mainly within the cleavage planes, results in distinct γ values along different directions.5 The large anharmonicity and low cutoff frequency of the LA branch, together with the low group velocities and orientational anharmonicity of the TA branches, would substantially limit heat transport and contribute to the low κL of CdSb. Given the phonon group velocities, averaged mode Grüneisen parameters, and Debye temperatures for the three acoustic phonon branches (listed in Table 2), temperature dependence of κL of CdSb is calculated using the DebyeCallaway implementation reported in ref 86 and shown as the solid line in Figure 4b. Despite showing slightly higher values, the calculated line without considering other scatterings (impurity scattering, etc.) shows reasonable agreement with the experimental κL, which also implies that low κL is intrinsic to CdSb. 1078



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Figure 8. Temperature dependences of thermoelectric figure of merit ZT for Cd1−xAgxSb, (a) in comparison of the best ZT in this study with those of some state-of-the-art thermoelectric materials (b).

located at the X point and ∼0.06 eV below VBM, and both bands show nonparabolic shapes. The conduction band minimum (CBM) appears in the Γ−Z direction, and several conduction band valleys can be observed along the Γ−X and Γ−Y directions. From the DOS and the projected band structures of Cd and Sb around the Fermi level shown in Figure 6b−d, it can be seen that the upper part of the valence band is predominately contributed by the p-orbitals of Sb with slight hybridization with the Cd p-orbitals (minor contribution of sorbitals of both atoms), which is consistent with the X-ray spectroscopy results.92 The s,p hybridization of Cd and Sb atomic orbitals creates the CBM. Sb 5s2 electrons, however, mainly contribute to the isolated bands, deep in the valence band (two lowest elemental bands shown in Figure 6a). For ptype CdSb, the predominance of Sb in the upper valence band also suggests that doping at the Cd sites would be an effective way to adjust hole concentration without significant alteration of the upper valence band structure. The high temperature electrical transport properties (300− 600 K) of Cd1−xAgxSb are shown in Figure 7. The undoped sample shows low electrical conductivity but high Seebeck coefficient α (∼400 μV/K at 300 K), consistent with the results of previously reported single crystals.25,51 Ag-doping significantly increases the electrical conductivity but decreases Seebeck coefficient due to the increased hole concentration. The increased hole concentration also visibly suppresses the bipolar transport, as evident by a shift of the maximum Seebeck coefficient or the minimum electrical conductivity to higher temperatures. The energy gap estimated using the equation Eg ≈ 2eαmaxTmax is 0.25−0.32 eV,93 much smaller than the reported 300 K value of 0.45−0.5 eV.25,89 The temperaturedependent band gap of CdSb can be expressed as Eg(T) = (0.63 − 6 × 10−4 T/K) eV; thus, the band gap decreases rapidly from 0.45 eV at 300 K to 0.27 eV at 600 K.25,89 The decreased band gap well accounts for the bipolar transport at elevated temperatures. Room temperature hole effective mass shown in Table 1 increases monotonically with increasing hole concentration, indicating a nonparabolic valence band, which is consistent with our band structure calculations. The room temperature Seebeck coefficient versus hole concentration is shown in Figure 7c, and the solid line is calculated based on the band structure shown in Figure 6a and the Boltzmann transport theory under a rigid band approximation.94 α-pH data for the Ag-doped samples fit well with the calculated line; though a

large deviation can be observed for the undoped sample, presumably due to the influence of the minority carriers. This indicates that Ag-doping on the Cd sites shows negligible influence on the valence band structure, which corroborates the fact that the upper valence band is mainly contributed by Sb. Ag-doping significantly improves the power factor (α2σ), as shown in Figure 7d. The maximum power factor reaches 20 μW/cm K2, comparable to those of optimized PbTe-based compounds.95 The high power factor is attributable to the low ionicity, which ensures high carrier mobility or weighted mobility, as well as optimized carrier concentration by Agdoping. Compared with the power factors of heavily doped single crystals (as high as 35 μW/cm K2 along the c axis),36 our polycrystals show lower values because the intensified impurity scattering as well as randomized grain orientations both significantly lower hole mobility. 2.5. Dimensionless Figure of Merit. The temperature dependences of dimensionless figure of merit ZT = α2σT/κ for Cd1−xAgxSb are plotted in Figure 8a. The undoped sample shows a low ZT of ∼0.35 due to its very low carrier concentration. Ag-doping effectively increases the hole concentration and significantly enhances ZT to 1.1 for the x = 0.1 at. % sample and further to 1.3 at 560 K for the x = 0.5 at. % sample. The best average ZT between 300 K and 600 K reaches 1.0, which is comparable to the best results for p-type thermoelectric materials in this temperature range. The high ZT in these materials is intrinsic and originated from covalent bonding with weakly anisotropic multicenter arrangement (high carrier weighted mobility) and large lattice anharmonicity (low κL) and is thus robust and easily reproduced. In addition, we compare the temperature dependence of ZT of some stateof-the-art p-type thermoelectric materials including p-type (Bi,Sb)2Te3,56 p-type Zn4Sb3,96 p-type skutterudites (SKs),97 and p-type PbTe,98 as shown in Figure 8b. It is noted that the Ag-doped CdSb shows high ZT values between 400 K and 600 K, at which ZT values of Bi2Te3-based materials decrease rapidly with increasing temperature due to their small band gaps and p-type PbTe-based materials or p-type skutterudites still display low ZTs owing to their wider band gaps. The high average ZT and its good reproducibility render CdSb a promising candidate for low−medium temperature power generations (400−600 K) or multistage devices. In addition, CdSb can also be doped into n-type materials, such as III−A group doping at the Cd sites or VI−A group doping at the Sb 1079



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sites,49 which would enable it practical for module fabrications. The toxicity of Cd, however, is an issue for wide-range application of these compounds, which needs proper safety engineering in the production processes and good insulation of the devices.

Research Program (973-program) of China under Project No. 2013CB632501, and NSFC Grant 11234012.

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3. CONCLUSIONS P-type polycrystalline Cd1−xAgxSb (0 ≤ x ≤ 0.1) samples were prepared by a melting−annealing−spark plasma sintering technique. A highest ZT value of 1.3 at 560 K and an average ZT value of 1.0 between 300 K and 600 K were achieved for x = 0.005, which makes this material promising for low−medium temperature thermoelectric applications (400−600 K). The high thermoelectric performance is attributed to the intrinsically high carrier weighted mobility and low κL. High weighted mobility, which originates from low ionicity caused by the anisotropic multicenter bonds, facilitates excellent power factor enabled by effective adjustment of hole concentration via Agdoping. Meanwhile, the localized electrostatic distortion and special spatial distribution of charge density in between cleavage layers not only endow soft chemical bonding, but also cause large lattice anharmonicity. These, together with significantly low cutoff frequency of the LA branch through couplings with low-lying optical phonons, give rise to a very low κL approaching the minimum value of CdSb. The unique lattice dynamics and low ionicity in electron-demand systems with anisotropic multicenter bonding reveal a new avenue in identifying new compounds with simple structures for thermoelectric applications.

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ASSOCIATED CONTENT

S Supporting Information *

The experimental and computational techniques; the powder XRD; the phase diagram of Cd−Sb binary system; calculated lattice parameters; the back scattering image and elemental mappings of Cd, Sb, Ag of the x = 0.5 at. % sample; the backscattered electron imagines (BEIs) of the x = 0.0, 0.1 at. %, 0.3 at. %, and 1 at. % samples; the SEM pictures of fractural surfaces of the x = 0.5 at. % sample; anisotropy studies of thermoelectric properties of the x = 0.5 at. % sample; carrier concentration as a function of Ag nominal composition; heat capacity measured by ratio method for thermal conductivity calculations; the comparisons of lattice thermal conductivity of CdSb with some binary compounds; the cycle studies of the x = 0.5 at. % sample. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Author Contributions ⊥

S.W. and J.Y. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by U.S. Department of Energy under Corporate Agreement No. DE-FC26-04NT42278, by GM, and by the National Science Foundation under Award No. 1235535. W.Z. is also partially supported by National Basic 1080



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Anisotropic Multicenter Bonding and High Thermoelectric

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